# Is there a magnetic field around a moving single charge?

## Main Question or Discussion Point

is there a magnetic field around a moving "single" charge?

Quote: "All moving charged particles produce magnetic fields."

Hypothetically - if you took a bunch of charged hydrogen ions (H+) and moved them through space, would there be a magnetic field around them? (ie, there are no electrons anywhere in this experiment, only protons)

From what I understand, a magnetic field only occurs when you have electrons amidst the positively charge protons such that - relatively speaking - in the case of a current, the electrons are moving one direction while the protons move the other.

Thanks!!
:)

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Dale
Mentor

Yes, there would be a magnetic field around an isolated moving charge.

Consider that current - an element of Maxwell's equations for electromagnetism - is measured as charge-per-unit-time, moving across an arbitrary boundary.

The nature of the current-bearing elements don't matter. Protons are fine, or alpha particles (helium nuclei +2) they make a dandy magnetic current as they dash off.

bcrowell
Staff Emeritus
Gold Member

It certainly makes a magnetic field. An easy way to prove this is that under a Lorentz transformation, a pure electric field becomes a mixture of electric and magnetic fields.

What you have to watch out for is the assumption that this is "the" field of an infinitesimal element of current. Maxwell's equations imply charge conservation, but an isolated infinitesimal element of current violates charge conservation.

It certainly makes a magnetic field. An easy way to prove this is that under a Lorentz transformation, a pure electric field becomes a mixture of electric and magnetic fields.

What you have to watch out for is the assumption that this is "the" field of an infinitesimal element of current. Maxwell's equations imply charge conservation, but an isolated infinitesimal element of current violates charge conservation.
Oooh! Whenever someone thinks like me, it's a clear sign of brilliance, I figure.

There aren't many examples of discussing electrostatics, so I'd started a thread called Postulate: EVERY field has a "magnetic" equivalent. under General Relativity,
and you'll see my cleverness is only rivaled by my humility. And modesty.

Anyhow, I agree thoroughly that electricity and magnetism are a unity with apparent differences, due principally to our frames of reference.